Please assist me in solving this microeconomic question. Thank you

(i)(a) Show that the adjustment coefficient for a compound Poisson claims process satisfies the inequality: r - 2[c/ 1 - E(X)] E(X' ) and define what each of the symbols represents. (i)(b) Explain how this inequality provides information about the probability of ultimate ruin for the process. (ii) An insurer considers that claims of a certain type occur in accordance with a compound Poisson process. The claim frequency for the whole portfolio is 100 per annum and individual claims have an exponential distribution with a mean of EX, DOO. (a) Calculate the adjustment coefficient if the total premium rate for the portfolio is f1,000,000 per annum. (h) Verify that the value calculated in (ii)(a) satisfies the inequality in (i)(a). (c) The insurer decides to take out excess of loss reinsurance for this portfolio. The reinsurer has agreed to pay the excess of any individual claim above $20.000 in return for an annual premium of $80.090. Calculate the adjustment coefficient for the direct insurer when the reinsurance is in operation. () Estimate the direct insurer's probability of ultimate ruin with and without the reinsurance arrangement, assuming that the initial surplus is $20,000 and that future premiums remain at the same level. (e) Comment briefly on the effect of the reinsurance on the probability of ruin. [14] [Total 24]